Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros |
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Authors: | V N Dubinin |
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Institution: | (1) Institute of Applied Mathematics, Far-Eeastern Branch of the Russian Academy of Sciences, Vladivostock, Russia |
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Abstract: | It is shown that new inequalities for certain classes of entire functions can be obtained by applying the Schwarz lemma and
its generalizations to specially constructed Blaschke products. In particular, for entire functions of exponential type whose
zeros lie in the closed lower half-plane, distortion theorems, including the two-point distortion theorem on the real axis,
are proved. Similar results are established for polynomials with zeros in the closed unit disk. The classical theorems by
Turan and Ankeny-Rivlin are refined. In addition, a theorem on the mutual disposition of the zeros and critical points of
a polynomial is proved. Bibliography: 16 titles.
Dedicated to the 100th anniversary of G. M. Goluzin’s birthday
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 101–112. |
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Keywords: | |
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